Solid-state lasers are known in the art. Their laser gain media are dopant ions incorporated in dilute concentrations in solid hosts. The laser gain medium can be optically excited to emit electromagnetic radiation by impinging a pumping beam on the laser gain medium. In order to achieve the highest possible pumping efficiency or, equivalently, the highest possible small-signal gain, the intensity of the pumping beam must be high over a large distance in the laser gain medium. This can be achieved by using a focused diffraction-limited pumping beam, e.g., a fundamental TEM.sub.00 mode of a pumping laser. However, lasers emitting diffraction-limited beams are expensive and take up a large space. Because of these disadvantages, it is desirable to use non-diffraction-limited pumping beams originating from other pumping sources.
For efficient optical pumping, the overlap of the pumping beam with the laser mode must generally be high over the absorption length in the laser gain medium. For this purpose, it is known to set the confocal parameter of the pumping beam approximately equal to the absorption length of the laser gain medium, which is called mode matching. However, the filling of this mode matching condition brings in the following disadvantages. The pumping-beam waist must be above a certain lower limit, to which the laser-mode waist must be matched. If the pumping-beam waist is too small, higher-order spatial modes are excited in the laser resonator, and if it is too large, the small-signal gain decreases, the laser threshold increases, and the laser is either not very efficient or does not even reach threshold. As the pumping-beam waist and the laser-mode waist are increased, the small-signal gain decreases, and the laser threshold also increases; this renders difficult or even impossible the construction of an efficient laser with high output power from a low-power pumping laser. As is shown below, these difficulties have even more serious consequences for the construction of a pulsed mode locked laser.
Lasers emitting short or ultrashort pulses are important tools in a wide variety of applications in physics, chemistry, biology and medicine. A well-known technique for short or ultrashort pulse generation is mode locking. Mode locking is a coherent superposition of longitudinal laser cavity modes. It is forced by a temporal loss modulation which reduces the intracavity losses for a pulse within each cavity-roundtrip time. This results in an open net gain window, in which pulses only experience gain if they pass the modulator every cavity roundtrip time. The loss modulation can be formed either actively or passively. Active mode locking is achieved, for instance, using an acousto-optic modulator as an intracavity element, which is synchronized to the cavity-round trip time. However, short-pulse generation (in the femtosecond range) relies on passive mode locking techniques, because only a passive shutter is fast enough to shape and stabilize ultrashort pulses.
Ultra-fast passively mode locked solid-state lasers such as Ti:sapphire lasers typically use Kerr-lens mode locking. In Kerr-lens mode locking, self-focusing of the laser beam due to the Kerr effect combined with either a hard aperture or a "soft" gain aperture produces a self amplitude modulation. Kerr-lens mode locking has two main disadvantages. First, in order to achieve strong self-focusing, high pulse powers within the resonator are required. For this purpose, pumping lasers with high output powers of typically more than 3 W at wavelengths of about 500 nm have to be used. Second, a high overlap of the resonator mode and the pumping beam over a large distance, i.e., good mode matching, is required. As described above, fulfilling the mode matching condition for non-diffraction-limited pumping beams causes problems for continuous-wave lasers. For Kerr-lens-mode locked lasers, these problems are even more serious. Additionally, if the pumping-beam waist is increased, the intra-cavity intensity decreases due to decrease of the small-signal gain and because the laser-mode waist is larger. Therefore, the nonlinear Kerr effect is strongly reduced, which makes Kerr-lens mode locking very difficult. Moreover, nonlinear aperturing in the laser gain material also decreases due to the larger laser-mode waist, further weakening the Kerr-lens mode locking.
The mode matching requirement is critical especially for mode locked Ti:sapphire lasers because of the relatively small gain in the Ti:sapphire crystal. For a high overlap, a high pumping-beam quality, a high pumping-beam stability, a precise resonator adjustment and a high resonator stability are necessary. Consequently, Kerr-lens mode locked lasers must be pumped with a pumping laser emitting its fundamental TEM.sub.00 mode and being diffraction-limited, i.e., having a coefficient of beam quality M.sup.2 .about.1. They are relatively expensive and scarecely suitable for non-laboratory applications.
Passive mode locking can also be achieved with semiconductor saturable absorber mirrors. A semiconductor saturable absorber mirror is a nonlinear mirror inserted inside the laser cavity. Its reflectivity is higher at higher light intensities due to absorption bleaching obtained by using semiconductors as the nonlinear material. A semiconductor saturable absorber mirror typically consists of a bottom mirror, the saturable absorber structure and, optionally, an additional antireflection or high-reflection coating on the top.
In this document, the following physical concepts are used.
1. The coefficient of beam quality M.sup.2 (cf. T. F. Johnston, Jr., "M.sup.2 concept characterizes beam quality", Laser Focus World, May 1990) of a light beam propagating in a medium is defined as EQU M.sup.2 =(.pi.n/4).multidot..theta..multidot.(2w.sub.0)/.lambda., PA0 2. The confocal parameter of a light beam is defined as EQU b=(.pi.n/2).multidot.(2w.sub.0).sup.2 /(M.sup.2 .lambda.)=4w.sub.0 /.theta. . PA0 3. The absorption length L.sub.a of a medium for light of a given wavelength is defined as EQU L.sub.a =1/.alpha., PA0 4. The product .delta..tau. of the stimulated emission cross section a and the spontaneous fluorescence lifetime .tau. is characteristic for a certain material at a given wave-length. A laser-gain medium with a large product .sigma..tau. yields high figures of merit.
wherein n is the refraction index of the medium, .theta. is the beam divergence angle, 2w.sub.0 is the waist diameter and .lambda. is the vacuum wavelength of the beam. M.sup.2 =1 for a diffraction-limited fundamental laser mode, and it increases for modes of greater divergence or greater focal area.
wherein .alpha. is the absorption coefficient of the medium and is defined by the equation EQU I(x)=I(0).multidot.e.sup.-.alpha.x,
I(0) being the incoming light intensity and I(x) being the light intensity after a penetration depth x.